feols {fixest} | R Documentation

## Fixed-effects OLS estimation

### Description

Estimates OLS with any number of fixed-effects.

### Usage

    feols(fml, data, weights, offset, fixef, fixef.tol = 1e-07,
      fixef.iter = 2000, na_inf.rm = getFixest_na_inf.rm(),
      nthreads = getFixest_nthreads(), verbose = 0, warn = TRUE,
      notes = getFixest_notes(), combine.quick, ...)

### Arguments

`fml`

A formula representing the relation to be estimated. For example: `fml = z~x+y`. To include fixed-effects, insert them in this formula using a pipe: e.g. `fml = z~x+y | fe_1+fe_2`. You can combine two clusters with `^`: e.g. `fml = z~x+y|fe_1^fe_2`, see details. You can also use variables with varying slopes using square brackets: e.g. in `fml = z~y|fe_1[x] + fe_2` the variable `x` will have one coefficient for each value of `fe_1` – if you use varying slopes, please have a look at the details section (can't describe it all here).

`data` | A data.frame containing the necessary variables to run the model. The variables of the non-linear right hand side of the formula are identified with this `data.frame` names. Can also be a matrix.
`weights` | A formula or a numeric vector. Each observation can be weighted, the weights must be greater than 0. If equal to a formula, it should be of one-sided: for example `~ var_weight`.
`offset` | A formula or a numeric vector. An offset can be added to the estimation. If equal to a formula, it should be of the form (for example) `~0.5*x**2`. This offset is linearly added to the elements of the main formula 'fml'.
`fixef` | Character vector. The name/s of a/some variable/s within the dataset to be used as fixed-effects. These variables should contain the identifier of each observation (e.g., think of it as a panel identifier).
`fixef.tol` | Precision used to obtain the fixed-effects (ie cluster coefficients). Defaults to `1e-5`. It corresponds to the maximum absolute difference allowed between two coefficients of successive iterations. Argument `fixef.tol` cannot be lower than `10000*.Machine$double.eps`. Note that this parameter is dynamically controlled by the algorithm.
`fixef.iter` | Maximum number of iterations in the step obtaining the fixed-effects (only in use for 2+ clusters). Default is 10000.
`na_inf.rm` | Logical, default is `TRUE`. If the variables necessary for the estimation contain NA/Infs and `na_inf.rm = TRUE`, then all observations containing NA are removed prior to estimation and a note is displayed detailing the number of observations removed. Otherwise, an error is raised.
`nthreads` | Integer: Number of nthreads to be used (accelerates the algorithm via the use of openMP routines). The default is to use the total number of nthreads available minus two. You can set permanently the number of nthreads used within this package using the function `setFixest_nthreads`.
`verbose` | Integer, default is 0. It represents the level of information that should be reported during the optimisation process. If `verbose=0`: nothing is reported. If `verbose=1`: the value of the coefficients and the likelihood are reported. If `verbose=2`: `1` + information on the computing time of the null model, the cluster coefficients and the hessian are reported.
`warn` | Logical, default is `TRUE`. Whether warnings should be displayed (concerns warnings relating to: convergence state, collinearity issues and observation removal due to only 0/1 outcomes or presence of NA values).
`notes` | Logical. By default, two notes are displayed: when NAs are removed (to show additional information) and when some observations are removed because of only 0 (or 0/1) outcomes in a fixed-effect (in Poisson/Neg. Bin./Logit models). To avoid displaying these messages, you can set `notes = FALSE`. You can remove these messages permanently by using `setFixest_notes(FALSE)`.

`combine.quick`

Logical. When you combine different variables to transform them into a single fixed-effects you can do e.g. `y ~ x | paste(var1, var2)`. The algorithm provides a shorthand to do the same operation: `y ~ x | var1^var2`. Because pasting variables is a costly operation, the internal algorithm may use a numerical trick to hasten the process. The cost of doing so is that you lose the labels. If you are interested in getting the value of the fixed-effects coefficients after the estimation, you should use `combine.quick = FALSE`. By default it is equal to `FALSE` if the number of observations is lower than 50,000, and to `TRUE` otherwise.

`...` | Not currently used.

### Details

The method used to demean each variable along the fixed-effects is based on Berge (2018), since this is the same problem to solve as for the Gaussian case in a ML setup.

### Combining the fixed-effects

You can combine two variables to make it a new fixed-effect using `^`. The syntax is as follows: `fe_1^fe_2`. Here you created a new variable which is the combination of the two variables fe_1 and fe_2. This is identical to doing `paste0(fe_1, "_", fe_2)` but more convenient.

Note that pasting is a costly operation, especially for large data sets. Thus, the internal algorithm uses a numerical trick which is fast, but the drawback is that the identity of each observation is lost (i.e. they are now equal to a meaningless number instead of being equal to `paste0(fe_1, "_", fe_2)`). These “identities” are useful only if you're interested in the value of the fixed-effects (that you can extract with `fixef.fixest`). If you're only interested in coefficients of the variables, it doesn't matter. Anyway, you can use `combine.quick = FALSE` to tell the internal algorithm to use `paste` instead of the numerical trick. By default, the numerical trick is performed only for large data sets.

### Varying slopes

You can add variables with varying slopes in the fixed-effect part of the formula. The syntax is as follows: cluster_var[var1, var2]. Here the variables var1 and var2 will be with varying slopes (one slope per value in cluster_var) and the fixed-effect cluster_var will also be added.

To add only the variables with varying slopes and not the fixed-effect, use double square brackets: cluster_var[[var1, var2]].

In other words:

- cluster_var[var1, var2] is equivalent to cluster_var + cluster_var[[var1]] + cluster_var[[var2]]

- cluster_var[[var1, var2]] is equivalent to cluster_var[[var1]] + cluster_var[[var2]]

@seealso See also `summary.fixest` to see the results with the appropriate standard-errors, `fixef.fixest` to extract the cluster coefficients, and the functions `esttable` and `esttex` to visualize the results of multiple estimations. And other estimation methods: `femlm`, `feglm`, `fepois`, `fenegbin`, `feNmlm`.

### Author(s)

Laurent Berge

### References

Berge, Laurent, 2018, "Efficient estimation of maximum likelihood models with multiple fixed-effects: the R package FENmlm." CREA Discussion Papers, 13 (https://wwwen.uni.lu/content/download/110162/1299525/file/2018_13).

For models with multiple fixed-effects:

Gaure, Simen, 2013, "OLS with multiple high dimensional category variables", Computational Statistics & Data Analysis 66 pp. 8–18

### Examples

    # just one set of fixed-effects:
    res = feols(Sepal.Length ~ Sepal.Width + Petal.Length | Species, iris)
    summary(res)

    # now with varying slopes:
    res = feols(Sepal.Length ~ Petal.Length | Species[Sepal.Width], iris)
    summary(res)

    # combining the FEs
    base = iris
    base$fe_2 = rep(1:10, 15)
    res_comb = feols(Sepal.Length ~ Petal.Length | Species^fe_2, base)
    summary(res_comb)
    fixef(res_comb)[[1]]

[Package fixest version 0.1.0 Index]